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Modeling Multiday Extreme Precipitation Across Eastern Australia: A Dynamical Perspective

Ruethaichanok Kardkasem, Meagan Carney

Abstract

The purpose of this paper is to illustrate new techniques for computing multiday extreme precipitation taken from recent theoretical advancements in extreme value theory in the framework of dynamical systems, using historical precipitation data along the eastern coast of Australia as a case study. We explore the numerical pitfalls of applying standard extreme value techniques to model multiday extremes. Then, we illustrate that our data conforms to the appropriate setting for the application of recently derived extreme value distributions for runs of extremes in the dynamical framework and adapt these to the non-stationary setting. Finally, we use these distributions to make more informed predictions on the return times and magnitudes of consecutive daily extreme precipitation and find changes in the dependence of increasing consecutive daily rainfall extremes on the Southern Oscillation Index. Although our case study is focused on extreme precipitation across eastern Australia, we emphasize that these techniques can be used to model expected returns and magnitudes of consecutive extreme precipitation events across many locations.

Modeling Multiday Extreme Precipitation Across Eastern Australia: A Dynamical Perspective

Abstract

The purpose of this paper is to illustrate new techniques for computing multiday extreme precipitation taken from recent theoretical advancements in extreme value theory in the framework of dynamical systems, using historical precipitation data along the eastern coast of Australia as a case study. We explore the numerical pitfalls of applying standard extreme value techniques to model multiday extremes. Then, we illustrate that our data conforms to the appropriate setting for the application of recently derived extreme value distributions for runs of extremes in the dynamical framework and adapt these to the non-stationary setting. Finally, we use these distributions to make more informed predictions on the return times and magnitudes of consecutive daily extreme precipitation and find changes in the dependence of increasing consecutive daily rainfall extremes on the Southern Oscillation Index. Although our case study is focused on extreme precipitation across eastern Australia, we emphasize that these techniques can be used to model expected returns and magnitudes of consecutive extreme precipitation events across many locations.
Paper Structure (4 sections, 2 theorems, 13 equations, 7 figures, 4 tables)

This paper contains 4 sections, 2 theorems, 13 equations, 7 figures, 4 tables.

Table of Contents

  1. Introduction and Background
  2. Data and Methodology
  3. Results and Conclusions
  4. Supplementary figures and tables

Key Result

Theorem 1.1

Given any weakly dependent sequence with extremal index $\theta$ and GEV, $G_2(\mu^*,\sigma^*,\xi)$, there exists a GEV, $G(\mu,\sigma,\xi)$ for a corresponding independent sequence such that, where the extremal parameters of $G_2$ and $G$ are related by,

Figures (7)

  • Figure 1: Ferro-Segers extremal index estimate for daily rainfall from stations across eastern Australia.
  • Figure 2: Shape parameter estimate of the GEV for $B_{i,m}$ for increasing window size. Longer block lengths are able to capture the true shape parameter for greater window sizes.
  • Figure 3: 2022 return levels, 10-years out from 2011 and 20-years out from 2001, for mutliday extreme rainfall across stations in eastern Australia for $k = 1$, $k = 2$, and $k = 3$ consecutive days (from top).
  • Figure 4: Example simulated SOI from randomly sampling from the distribution of averaged yearly historical SOI.
  • Figure 5: From the left to right, 20-, 40-, and 100-year return levels for (top to bottom) $k=1$, 2, and 3 consecutive days of extreme rainfall.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Definition 1
  • Definition 2
  • Theorem 1.1: Coles Coles2001
  • Lemma 1.2: Lemma 4.1 CHNT
  • Remark 2.1
  • Remark 2.2